Boys sometimes handicap themselves in order to show off to girls. They ride bicycles with no hands, they get drunk and take risks and they engage in costly displays of public generosity. The handicap principle suggests that public charitable donations will often be made by men.
Ladies also adopt cultural handicaps. They wear high-heeled shoes, crush their waists using corsets, bind their feet, conceal their faces and mutilate themselves.
Cultural handicaps are celebrated in popular culture. Inigo Montoya and The Man in Black both fight with their left hand in The Princess Bride. Luke Skywalker fights blindfold in Star Wars, A New Hope.
Cultural handicaps are also used in the game of go - where one player disables himself in order to have a fair fight with another. Handicapping is common in sports. There's a Wikipedia page about the topic.
Many ostentatious social norm violations could be seen as being handicaps. Real men wear pink is one example.
So far, cultural handicaps do not appear to have received the same level of study as organic handicaps. This is probably because of the immature state of the science of cultural evolution.